Nobody is proposing that tax dollars be used to fund a colony. Elon is says he's planning on doing that using profits from SpaceX's other business.
I'm not aware of anyone every proposing that people mine minerals on Mars for shipment back to Earth. I have heard people talk about using propellant made on Mars to fuel voyages further out, Zubrin is big on that idea, but that's another kettle of fish - energy and mass can cost different amounts in different places.
People sometimes talk about mining asteroids and bringing the resulting minerals to Earth. I'm not sure that that is economically feasible, at least right now, but it avoids the big problem of having to launch stuff out of Mars's gravity well. Technically speaking the energy involved in getting an asteroid from the main belt to Earth is steeply negative so I don't think you could say that it's impossible on a strictly energy accounting basis, especially since there's no fixed rule establishing the relative value of energy and matter across different technological regimes.
But right now we spend huge amount of energy lofting satellites into orbit around the Earth. If we could use material that was already in space to build satellites in orbit that would be much cheaper from a strictly energy accounting standpoint. That would, of course, require some technological advances but makes a lot of sense if you just look at it in terms of energy.